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We present three equivalent definitions of S¹-equivariant symplectic homology. We show that, using rational coefficients, the positive part of S¹-equivariant symplectic homology is isomorphic to linearized contact homology when the latter is defined. We present several computations and applications, and introduce a substitute for cylindrical/linearized contact homology based on an S¹-equivariant construction. [ABSTRACT FROM AUTHOR]

We show that, for every contact manifold M and for every Riemann surface Σ of genus at least 1, the manifold Σ × M admits a contact structure. In particular, the tori T2n+1 are contact manifolds. [ABSTRACT FROM AUTHOR]